Transport properties of a Luttinger liquid with a cluster of impurities

In this work, the correlation functions of a Luttinger liquid with a cluster of impurities around an origin obtained using the non-chiral bosonization technique (NCBT) are used to study temperature dependence of tunneling conductance. This temperature dependence is shown to be a simple power law when the forward-scattering mutual interaction between fermions is short-ranged and has a large bandwidth (relative to temperature). Special attention is paid to the nature of the exponent in this power law for situations close to resonant tunneling (eg. in case of double barrier). A distinction is made between Kubo conductance which is related to current - current correlation (a four-point function) and the tunneling conductance which is the outcome of a tunneling experiment (related to two-point functions). In both the cases, closed analytical expressions for conductance are calculated at temperatures small compared to the bandwidth and a number of interesting physical properties are discussed, besides presenting a favorable comparison with existing literature. The novelty of this work are the closed analytical formulas for the conductance exponents for arbitrary strengths of impurities and mutual interaction between fermions.